Learn Finnish: Voitko saada minut uskomaan tähän hallusinaatioon? - Can you get me to believe in this hallucination?

This sentence uses the causative structure where saada means "to get someone to do something". In this structure, the action the person is caused to do must be in the 3rd infinitive illative form, ending in -maan or -mään. Thus, saada minut uskomaan translates to "to get me to believe".

Why is the pronoun minut in the accusative case instead of the partitive minua?

In the saada + object + 3rd infinitive structure, the person being influenced is the direct object of the verb saada. Because the sentence implies aiming for a successful, completed result (actually getting the person to believe), the object takes the accusative case. For personal pronouns, this means using the special -t ending, hence minut.

Why are the words tähän and hallusinaatioon in the illative (into) case?

This is a strict rule (verb rection) for the verb uskoa. While English speakers say they believe "in" something, Finnish requires the illative case, as if you are believing "into" it. Both the pronoun tämä and the noun hallusinaatio must take this case to match the verb, becoming tähän hallusinaatioon.